Treball Final de Grau en Matemàtica Computacional. Codi: MT1030. Curs: 2019/2020Nowadays, we have powerful computers capable of performing very complex operations in seconds. However, there are problems that cannot be
addressed at reasonable execution times, such as NP-Complete problems.
For these problems no polynomial solution is known, having all of them
exponential cost, which makes them unfeasible for classical computers.
Quantum properties have impressed equally to computer scientists, physicist
and all kinds of scientists since they were discovered, since they are very unintuitive. However, these properties, such as entanglement or superposition,
lead us to have quantum computers and quantum algorithms that are able to
solve in polynomial time some of the NP-Complete problems. This would be
a breakthrough in fields with high computational demands such as machine
learning, medicine, chemistry, etc.
In this work, we will focus on knowing the computing mathematical basis
that will allow us to study the complex quantum world, which includes,
among other things, complex vector spaces and complex algebra. We will
study the properties offered by the quantum computing world, such as the
superposition of states or entanglement. We will also see quantum gates
that will allow us to build quantum circuits to be able to create algorithms
that we can execute on our quantum computers. We will finish the work by
studying some well knows algorithms which will allow us to see how to take
advantage of the quantum properties to accelerate our computing capacit
